%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO098^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:46:36 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 19 unt; 0 typ; 7 def)
% Number of atoms : 252 ( 66 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 234 ( 36 ~; 30 |; 9 &; 146 @)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 60 !; 11 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ: $i > $i > $o ).
thf(func_def_1,type,
cR: $i > $i > $o ).
thf(func_def_6,type,
sF1: $i > $o ).
thf(func_def_7,type,
sF2: $i > $i > $o ).
thf(func_def_8,type,
sF3: $i > $i > $o ).
thf(func_def_9,type,
sF4: $o ).
thf(f1,conjecture,
( ! [X0: $i] :
~ ( cR @ X0 @ X0 )
=> ? [X1: $i,X2: $i] :
( ~ ( cR @ X1 @ X2 )
& ( ( cQ @ X2 @ X1 )
=> ! [X3: $i] : ( cQ @ X3 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM65) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
~ ( cR @ X0 @ X0 )
=> ? [X1: $i,X2: $i] :
( ~ ( cR @ X1 @ X2 )
& ( ( cQ @ X2 @ X1 )
=> ! [X3: $i] : ( cQ @ X3 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i] :
~ ( cR @ X0 @ X0 )
=> ? [X1: $i,X2: $i] :
( ~ ( cR @ X1 @ X2 )
& ( ( cQ @ X2 @ X1 )
=> ! [X3: $i] : ( cQ @ X3 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
=> ? [X1: $i,X2: $i] :
( ( ( cR @ X1 @ X2 )
!= $true )
& ( ( ( cQ @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( cQ @ X3 @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
=> ? [X1: $i,X2: $i] :
( ( ( ( cQ @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( cQ @ X3 @ X3 )
= $true ) )
& ( ( cR @ X1 @ X2 )
!= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
& ! [X1: $i,X2: $i] :
( ( ( ( cQ @ X2 @ X1 )
= $true )
& ? [X3: $i] :
( ( cQ @ X3 @ X3 )
!= $true ) )
| ( ( cR @ X1 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
& ! [X1: $i,X2: $i] :
( ( ( ( cQ @ X2 @ X1 )
= $true )
& ( ( cQ @ sK0 @ sK0 )
!= $true ) )
| ( ( cR @ X1 @ X2 )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0)],[f6]) ).
thf(f8,plain,
! [X2: $i,X1: $i] :
( ( ( cQ @ sK0 @ sK0 )
!= $true )
| ( ( cR @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X2: $i,X1: $i] :
( ( ( cQ @ X2 @ X1 )
= $true )
| ( ( cR @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,definition,
! [X0: $i] :
( ( sF1 @ X0 )
= ( cR @ X0 @ X0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f14,plain,
! [X0: $i] :
( ( cR @ X0 @ X0 )
= ( sF1 @ X0 ) ),
inference(reorient_equations,[],[f13]) ).
thf(f15,plain,
! [X0: $i] :
( $true
!= ( sF1 @ X0 ) ),
inference(definition_folding,[],[f10,f14]) ).
thf(f16,definition,
! [X2: $i,X1: $i] :
( ( sF2 @ X1 @ X2 )
= ( cQ @ X2 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f17,plain,
! [X2: $i,X1: $i] :
( ( cQ @ X2 @ X1 )
= ( sF2 @ X1 @ X2 ) ),
inference(reorient_equations,[],[f16]) ).
thf(f18,definition,
! [X2: $i,X1: $i] :
( ( sF3 @ X2 @ X1 )
= ( cR @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f19,plain,
! [X2: $i,X1: $i] :
( ( cR @ X1 @ X2 )
= ( sF3 @ X2 @ X1 ) ),
inference(reorient_equations,[],[f18]) ).
thf(f20,plain,
! [X2: $i,X1: $i] :
( ( ( sF3 @ X2 @ X1 )
= $true )
| ( ( sF2 @ X1 @ X2 )
= $true ) ),
inference(definition_folding,[],[f9,f19,f17]) ).
thf(f21,definition,
( sF4
= ( cQ @ sK0 @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f22,plain,
( ( cQ @ sK0 @ sK0 )
= sF4 ),
inference(reorient_equations,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( ( sF4 != $true )
| ( ( sF3 @ X2 @ X1 )
= $true ) ),
inference(definition_folding,[],[f8,f19,f22]) ).
thf(f24,plain,
! [X2: $i,X1: $i] :
( ( ( sF2 @ X1 @ X2 )
= $false )
| ( ( cQ @ X2 @ X1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f17]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( ( ( sF3 @ X2 @ X1 )
= $false )
| ( ( cR @ X1 @ X2 )
= $true ) ),
inference(iff_proxy_clausification,[],[f19]) ).
thf(f29,plain,
( ( ( cQ @ sK0 @ sK0 )
= $false )
| ( sF4 = $true ) ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f31,plain,
! [X0: $i] :
( ( ( cR @ X0 @ X0 )
= $false )
| ( $true
= ( sF1 @ X0 ) ) ),
inference(iff_proxy_clausification,[],[f14]) ).
thf(f33,definition,
( spl5_1
<=> ! [X2: $i,X1: $i] :
( ( sF3 @ X2 @ X1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f34,plain,
( ! [X2: $i,X1: $i] :
( ( sF3 @ X2 @ X1 )
= $true )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f36,definition,
( spl5_2
<=> ( sF4 = $true ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f39,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f23,f36,f33]) ).
thf(f41,definition,
( spl5_3
<=> ( ( cQ @ sK0 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f43,plain,
( ( ( cQ @ sK0 @ sK0 )
= $false )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f44,plain,
( spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f29,f36,f41]) ).
thf(f78,plain,
! [X0: $i] :
( ( cR @ X0 @ X0 )
= $false ),
inference(forward_subsumption_resolution,[],[f31,f15]) ).
thf(f87,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( cR @ X1 @ X0 ) )
| ( $true
= ( sF2 @ X1 @ X0 ) ) ),
inference(constrained_superposition,[],[f26,f20]) ).
thf(f90,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( sF2 @ X1 @ X0 ) )
| ( $true
= ( cR @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f93,plain,
! [X0: $i,X1: $i] :
( ( ( cQ @ X1 @ X0 )
= $true )
| ( ( cR @ X0 @ X1 )
= $true )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f90,f24]) ).
thf(f95,plain,
! [X0: $i,X1: $i] :
( ( ( cR @ X0 @ X1 )
= $true )
| ( ( cQ @ X1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f98,plain,
! [X0: $i] :
( ( $true
= ( cQ @ X0 @ X0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f78,f95]) ).
thf(f99,plain,
! [X0: $i] :
( $true
= ( cQ @ X0 @ X0 ) ),
inference(trivial_inequality_removal,[],[f98]) ).
thf(f102,plain,
( ( $true = $false )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f43,f99]) ).
thf(f105,plain,
( $false
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f102]) ).
thf(f106,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[],[f105]) ).
thf(f114,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( cR @ X1 @ X0 ) )
| ( $true = $false ) )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f26,f34]) ).
thf(f115,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( cR @ X1 @ X0 ) )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f118,plain,
( ( $true = $false )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f78,f115]) ).
thf(f121,plain,
( $false
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f122,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f121]) ).
cnf(s1,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s2,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f44]) ).
cnf(s7,plain,
~ spl5_3,
inference(sat_conversion,[],[f106]) ).
cnf(s11,plain,
~ spl5_1,
inference(sat_conversion,[],[f122]) ).
cnf(s12,plain,
spl5_2,
inference(rat,[],[s2,s7]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s12,s11]) ).
thf(f123,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO098^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:37:03 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.28 % (3753061)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (3753080)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.28 % (3753080)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.19/0.28 % (3753080)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2414419097:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.28 % (3753080) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3753061-3753080"...
% 0.19/0.28 % (3753080)...printing done.
% 0.19/0.28 % (3753080)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (3753080)------------------------------
% 0.19/0.28 % (3753080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3753080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3753080)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3753080)Termination reason: Refutation
% 0.19/0.28 % (3753080)Time elapsed: 0.003 s
% 0.19/0.28 % (3753080)Peak memory usage: 13 MB
% 0.19/0.28 % (3753080)Instructions burned: 6 (million)
% 0.19/0.28 % (3753061)Success in time 0.045 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------